Imagine that we have a before and after reading for each item in the
sample: for example we might have measured blood pressure before and
after administration of a new drug. We can't pool the results and compare
the means before and after the change, because each patient will have
a different baseline reading. Instead we calculate the difference between
before and after measurements in each patient, and calculate the mean
and standard deviation of the differences. To test whether a significant
change has taken place, we can then test the null-hypothesis that the
true mean is zero using the same procedure we used in the single sample
cases previously discussed.